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• Atc-arrays

Ulong-array-integer-index-okp

Check if an ACL2 integer is a valid index (i.e. in range) for an array of type unsigned long.

Signature

(ulong-array-integer-index-okp array index) → yes/no

Arguments

array — Guard (ulong-arrayp array).

index — Guard (integerp index).

Returns

yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: ulong-array-integer-index-okp

(defun ulong-array-integer-index-okp (array index)
  (declare (xargs :guard (and (ulong-arrayp array)
                              (integerp index))))
  (let ((__function__ 'ulong-array-integer-index-okp))
    (declare (ignorable __function__))
    (integer-range-p 0 (ulong-array-length array)
                     (ifix index))))

Theorem: booleanp-of-ulong-array-integer-index-okp

(defthm booleanp-of-ulong-array-integer-index-okp
  (b* ((yes/no (ulong-array-integer-index-okp array index)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: ulong-array-integer-index-okp-of-ulong-array-fix-array

(defthm ulong-array-integer-index-okp-of-ulong-array-fix-array
  (equal (ulong-array-integer-index-okp (ulong-array-fix array)
                                        index)
         (ulong-array-integer-index-okp array index)))

Theorem: ulong-array-integer-index-okp-ulong-array-equiv-congruence-on-array

(defthm
 ulong-array-integer-index-okp-ulong-array-equiv-congruence-on-array
 (implies (ulong-array-equiv array array-equiv)
          (equal (ulong-array-integer-index-okp array index)
                 (ulong-array-integer-index-okp array-equiv index)))
 :rule-classes :congruence)

Theorem: ulong-array-integer-index-okp-of-ifix-index

(defthm ulong-array-integer-index-okp-of-ifix-index
  (equal (ulong-array-integer-index-okp array (ifix index))
         (ulong-array-integer-index-okp array index)))

Theorem: ulong-array-integer-index-okp-int-equiv-congruence-on-index

(defthm ulong-array-integer-index-okp-int-equiv-congruence-on-index
 (implies (acl2::int-equiv index index-equiv)
          (equal (ulong-array-integer-index-okp array index)
                 (ulong-array-integer-index-okp array index-equiv)))
 :rule-classes :congruence)